# If $I \propto V$, then why is $R = V/I$ and not $I/V$?

I know that the current flowing through a conductor is directly proportional to the potential difference across its ends (by Ohm's Law). Hence,

• I ∝ V
• V ∝ I
• R = V/I, where R is a constant (Resistance)

But why can't it be derived this way?

• I ∝ V
• I = RV
• R = I/V

Won't these two derivations contradict each other?

Thank you

It is true that $$V/I$$ is a constant for resistors, and also that $$I/V$$ is a constant. But, of course, they are not the same constant.
$$R=V/I$$ gives the resistance of a resistor, while $$G=I/V$$ gives the less commonly-used conductance of a resistor.
Neither of these is a "derivation" of the resistance- $$R=V/I$$ is a definition of resistance, and you can use Ohm's law to prove that it is constant.